Continuity mistake: In the scene showing Groucho being chased across the cars as they enter the race course, in the shot from behind you see him running along the rail only to slip, the following shot is from the front and shows the same slip he's already made.

Continuity mistake: In front of the betting windows, Chico sells Groucho the code books and master code books, then tells him he needs the entire set of Breeder's Guide books. Groucho pulls out his money and said "Give me all four", but Chico hands him five books.